Claremont Center for the Mathematical Sciences

We prove that the sequence {P(n) cos(na)}, n = 1,2,... is completely uniformly distributed modulo 1 for any non-constant polynomial P and a such that cos(a) is transcendental. As a special case of this result, we prove that the sequence {n b^n} for n=0,1,2,... is uniformly distributed modulo 1 for any Salem number b of degree 4. This is joint work with D. Berend.

In this talk, we examine unitary multiplication operators on the spaces of measures on the circle. In particular, we examine when these operators are cyclic and when collections of these operators have common cyclic vectors. The techniques used here are classical and only a basic knowledge of real analysis (measure theory, singular and absolutely continuous functions, spaces) is needed to appreciate this talk.

In this first conversation I will introduce a result due to Krasnosel'skii-Rabinowitz and concerned with the existence of global bifurcation branches of solutions of problems containing linear and nonlinear terms. An application will be given to the existence of solutions of boundary value problems of the Sturm-Liouville type.